My Android phone will not stay off when I shut I down. I was told to go to application manager in settings. My Android phone shows no application manager in settings
If you're shutting the phone down (powering off), I doubt you'll find anything in the application manager that's going to cause it to be booting on its own.
What phone do you have? What version of Android is it running?
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Welcome to Android Central! If your phone keeps powering back on by itself after you shut it down, I'd suspect a problem with the Power button. Bring it to a repair shop.